Session: 07-23-01: 100th Anniversary of the Timoshenko-Ehrenfest Beam Model

Paper Number: 96660

96660 - Reduced Theories for Thick Shells 

Reduced theories for thick shells

M.A. De Rosa¹, M. Lippiello², I. Elishakoff³

¹School of Engineering, University of Basilicata, Viale dell'Ateneo Lucano 10, 85100, Potenza, Italy, maria.derosa@unibas.it

²Department of Structures for Engineering and Architecture, University of Naples "Federico II", Via Forno Vecchio 36, 80134 Napoli, Italy, maria.lippiello@unina.it

³Department of Ocean and Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431-0991, USA, elsihako@fau.edu

 

Abstract

The present paper is part of a previous research, started in [1] with the proposal to neglect an energetic term in the dynamic analysis of Timoshenko-Ehrenfest beams. The resulting reduced theory turned out to be both simpler and more reliable than the complete, classical, approach. Whereas the original idea was heuristically justified, a sounder variationally
consistent theory has been proposed in [2]. Later on, a similar assumption has been proposed for the dymamic analysis of Uflyand-Mindlin plates [3], leading to a simplified truncated theory where the rotational kinetic energy is considered to be a functionally of the bending rotation. A third and final step is given in the present paper, where the dynamic analysis of a shell is performed, in the presence of shear deformation and rotational inertia. Following the suggestion offered in [1-3], we
initially describe the classical theory, and subsequently we propose two alternative hypotheses that lead to two differences aspects of the energy terms. Applying the variational approach, two new different boundary problems are deduced, which are direct generalizations of what was done previously. Both theories can be easily specialized for beams and plates. In addition, the theory is also specialized for the case of cylindrical shell. For all three approaches and for a simplysupported beam case and rectangular plates with four edges simply-supported, the calculations are implemented through a software developed in Mathematica language [4]. Results are validated by comparison with those available in the literature. In all cases, the numerical results confirm the results obtained in the papers previous.

[1] I. Elishakoff. An Equation Both More Consistent and Simpler Than Bresse-Timoshenko Equation,in Advances in Math. Modeling and Experimental Methods for Materials and Structures (R. Gilat and L. Sills-Banks, eds.), 249-254, Springer Verlag, Berlin 2009.

[2] M.A. De Rosa, M. Lippiello, I. Elishakoff. Variational Derivation of Truncated Timoshenko-Ehrenfest Beam Theory. J. Appl. Comput. Mech., 8(3) (2022) 996-1004, DOI: 10.22055/jacm.2022.39354.3394.

[3] M.A. De Rosa, M. Lippiello, I. Elishakoff. An alternative formulation theory for truncated Uflyand- Mindlin plates models, to be appear Mathematics and Mechanics of solids.

[4] S. Wolfram. The Mathematica 8. Cambridge University Press, Cambridge 2010.

Presenting Author: Isaac Elishakoff Department of Ocean and Mechanical Engineering, Florida Atlantic University

Presenting Author Biography: Dr. Isaac Elishakoff serves as the Distinguished Research Professor in the Department of Ocean and Mechanical Engineering at Florida Atlantic University. He also holds a courtesy appointment as a Professor in the Department of Mathematical Sciences. He was born in Kutaisi, Republic of Georgia, Europe on February 9, 1944. Professor Elishakoff holds a Ph.D. in Dynamics and Strength of Machines from the Power Engineering Institute and Technical University in Moscow, Russia. Prior to joining the Florida Atlantic University, he taught one year in the Abkhazian University, Sukhumi, Republic of Georgia, and eighteen years at the Technion-Israel Institute of Technology in Haifa. He also occupied several visiting positions.<br/>Dr. Elishakoff has made pioneering contributions in several areas such as random vibrations, with special emphasis on continuous, homogeneous and composite beams, plates and shells and associated effects of refinements in theories and of cross- correlations; free vibration of structures with the generalization of Bolotin&#39;s dynamic edge effect method, free of degeneracy property characteristic to the original method; nonlinear<br/>buckling of structures, with a new method to combine the results of experimental measurements of shell imperfections to predict the theoretical knockdown factors associated with different manufacturing processes thus introducing, for the first time in the literature, the imperfection sensitivity concept into design; structural reliability with elucidation of errors associated with various low-order approximations and human errors;<br/>work on a non-probabilistic theory for treating uncertainty in mechanics, namely, optimization and anti-optimization under uncertainty and, especially, its combination with stochastic modeling; dynamic stability of structures with imperfections, in elastic or viscoelastic setting; random vibrations and reliability of composite structures with attendant first book worldwide; development of the improved finite element method for<br/>stochastic structures which has a non-perturbative nature; stochastic linearization; computerized symbolic algebra; co-authored the first and only monograph worldwide on convex modeling of uncertainty; co- authored the first and only monograph worldwide on reliability of composite structures; authored the first and only monograph on the Timoshenko-Ehrenfest beam theories in past 100 years that this theory exists.<br/>Dr. Elishakoff has published over 540 original papers in leading national and international journals and conference proceedings. His publications appeared mostly in ASME Journal of Applied Mechanics; Proceedings of the Royal Society of London; AIAA Journal; International Journal of Solids and Structures; Journal of Sound and Vibration;<br/>Journal Mathematical Problems in Engineering; Acta Mechanica; Journal of Composite Structures; Computer Methods in Applied Mechanics and Engineering; Computers and Structures; Journal of Acoustical Society of America; Chaos, Solitons &amp; Fractals; Meccanica; Philosophical Transactions of the Royal Society, and many others.

Authors:

Maria Anna De Rosa School of Engineering, University of Basilicata
Maria Lippiello Department of Structures for Engineering and Architecture, University of Naples "Federico II"
Isaac Elishakoff Department of Ocean and Mechanical Engineering, Florida Atlantic University